Profiling teacher pedagogical behaviours in plummeting postgraduate students’ anxiety in statistics

Abstract The indispensable relationship between Research and Statistics makes the teaching of both courses crucial in all postgraduate programmes. However, over the years, postgraduate students have displayed a high level of anxiety in studying Statistics. Therefore, exploiting the descriptive case study strategy knitted within the sequential explanatory design, a Statistics teacher was studied in one of Ghana’s outstanding universities and the reported pedagogical behaviours were profiled. Primary data were obtained from 99 postgraduate students (reading various postgraduate programmes on regular, sandwich and distance modes of education) on their level of anxiety in Statistics (using the Statistics Anxiety Rating Scale) and their experiences with their teacher’s pedagogical behaviours. Also, 12 of the postgraduate students were interviewed about the pedagogical behaviours of their teacher that reduced their anxiety in Statistics. To triangulate the primary data, secondary results on the teacher’s teaching practices were obtained from the Directorate of Academic Planning and Quality Assurance Unit of the university (originally gathered through a statistical academic support scale). Descriptive (mean and standard deviation) and inferential (one-way ANOVA and SEM) statistics were used to analyse the quantitative data and the qualitative data were analysed into themes. Consequently, the study found 17 teacher pedagogical behaviours under teacher characteristics (cognitive and affective factors) and pedagogical practices that reduced postgraduate students’ statistical anxiety and heightened positive attitudes towards the study of Statistics. Therefore, a recognition of these pedagogical behaviours and their open display during the teaching of Statistics will go a long way in reducing postgraduate students’ high statistical anxiety.

Prince Yeboah Asare is a Management Educator at the University of Cape Coast, Ghana, who holds PhD in Management Education, an MPhil in Curriculum and Teaching and a Bachelor's Degree in Management Education. He is a lecturer with research interests in Management Teacher Education, Curriculum and Teaching, Research Methods and Statistics. This current paper examined teacher pedagogical behaviours required to reduce postgraduate students' statistical anxiety. Future studies might explore nonclassroom factors that can reduce students' statistical anxiety and other related areas.

PUBLIC INTEREST STATEMENT
Higher education institutions have the mandate to develop critical minds (the ability to critically think will determine one's endurance to achieve competitive advantage over others), research and statistical skills in postgraduate students for the advancement of systems, structures and cultures in our societies. It is through research and statistical data analysis (if not partly) that knowledge is discovered for development. However, evidence across geographical contexts point out that postgraduate students are highly anxious about the study of Statistics. This creates a limiting factor to their appreciation and development of statistical skills. Previous studies have attributed the problem to the classroom behaviours of statistics teachers. The current study, therefore, focused on the pedagogical behaviours (characteristics and teaching practices) of statistics teachers that are required to reduce students' statistical anxiety. The paper provides 17 pedagogical behaviours under cognitive factors (e.g., content knowledge, practical statistical lessons, a critical explanation of technical terminologies), affective factors (e.g., teaching passion, teaching confidence, humour) and pedagogical practices (e.g., organise and systematic delivery, students engagement, effective communication) to address the problem.
postgraduate students were interviewed about the pedagogical behaviours of their teacher that reduced their anxiety in Statistics. To triangulate the primary data, secondary results on the teacher's teaching practices were obtained from the Directorate of Academic Planning and Quality Assurance Unit of the university (originally gathered through a statistical academic support scale). Descriptive (mean and standard deviation) and inferential (one-way ANOVA and SEM) statistics were used to analyse the quantitative data and the qualitative data were analysed into themes. Consequently, the study found 17 teacher pedagogical behaviours under teacher characteristics (cognitive and affective factors) and pedagogical practices that reduced postgraduate students' statistical anxiety and heightened positive attitudes towards the study of Statistics. Therefore, a recognition of these pedagogical behaviours and their open display during the teaching of Statistics will go a long way in reducing postgraduate students' high statistical anxiety.

Introduction
Postgraduate education follows the completion of an undergraduate degree at colleges and universities (Olibie et al., 2015). It awards postgraduate diplomas and certificates, masters and doctoral degrees. It aims to extend students' depth of knowledge in a particular field and develop on areas of expertise gained at the undergraduate level (House, 2010). Most importantly, postgraduate education is intended to develop learners to create new knowledge and to be innovative (Hénard & Roseveare, 2012), and to broaden students' academic abilities and engagement with research to help advance the course of society (Millberg et al., 2011). It is hoped that universities can raise skilled manpower required in a country (Çepni et al., 2018). Consequently, research is a formal area of study recognised in all well-grounded postgraduate education that helps to develop the aforementioned skills (Healey & Jenkins, 2009;Rose, 2005). Research is a global tool in the postgraduate education landscape equipping students with the necessary skills and knowledge to foster independent growth, creativity and lifelong researchers. Hence, "the nature and quality of research are inseparable from the nature and quality of postgraduate education and future education researchers" (Henson et al., 2010, p. 229). Therefore, it is not unusual that universities gain acceptance as respectable members of the global intellectual community through adherence to research credibility and capability standards (Jenkins, 2009).
Mostly, research requires good statistical knowledge for the transformation of research data (quantitative data) into relevant research results and findings to address identified problems in communities of study. The strong affinity that statistics lends to research has also made Statistics a compulsory course of study in all postgraduate education. Unequivocally, Statistics is a formidable course in the curriculum architecture of postgraduate studies (Onwuegbuzie & Leech, 2003). Postgraduate students cannot be well prepared for their coursework when Statistics course is excluded (Onwuegbuzie, 2004). Fisher (as cited in Aoun, 2018) has equally noted that statistical analysis is one of the top skills for most professional firms. This places a huge burden on university and college teachers on the quality delivery of Statistics courses and students' development of statistical knowledge and skills. Quality delivery of Statistics course highlights some managerial and pedagogical implications. The managerial implication requires academic departments to allow the right calibre of Statistics teachers to teach the course by paying attention to some specific pedagogical behaviours required to boost students' appreciation and understanding of Statistics.
By pedagogy, Statistics teachers will need to exhibit acceptable teaching characteristics and employ appropriate teaching practices, both conceptualised as pedagogical behaviours, which support students' understanding of Statistics. Pedagogical behaviours, as gleaned from Richter and Lara Herrera (2017), are the characteristics and practices that teachers manifestly display during instructional sessions. Klibthong and Agbenyega (2018) affirmed classroom practices as part of teachers' pedagogical behaviours and noted it as a key obstacle to curriculum implementation. Tang et al. (2020) considered it as the use of structured activities and time as well as methods employed by teachers in delivering subject content to students. Pedagogical behaviours refer to teachers' classroom dispositions (Loreman, 2013). Simply, pedagogy is the nexus between teaching and learning (Loughran, 2010;UNESCO, 2017) and pedagogical behaviours are the characteristics (teacher knowledge, patience, enthusiasm, etc.) and practices (planning lessons, involving learners, using questioning to promote thinking, monitoring and giving feedback, assessing process and performance, etc.) exhibited by teachers within the interaction of teaching and learning to facilitate students' acquisition of knowledge, attitude, values and skills.
Regrettably, postgraduate students' psychological and behavioural dispositions before and after studying Statistics impede the objective of developing lifelong researchers with strong statistical acumen. This psychological and behavioural phenomenon is described in the literature as students' anxiety in Statistics or statistical anxiety and defined broadly as: a performance characterized by extensive worry, intrusive thoughts, mental disorganization, tension, and physiological arousal . . . when exposed to statistics content, problems, instructional situations, or evaluative contexts, and is commonly claimed to debilitate performance in a wide variety of academic situations by interfering with the manipulation of statistics data and solution of statistics problems. (Zeidner, 1991, p. 319) Extensive empirical studies (e.g., Casinillo et al., 2022;Erfanmanesh et al., 2014;Onwuegbuzie, 2004;Chew et al., 2017;Ruggeri et al., 2008) have shown that postgraduate students are highly provoked by the study of Statistics. These evidence make the problem of students' statistical anxiety real and leave no doubts. It happens when students experience Statistics and the contents of Statistics courses; therefore, the condition is considered a state anxiety rather than a trait anxiety (Onwuegbuzie, 2004). The severity of students' statistical anxiety could be higher than anxiety experienced in other courses (Dykeman, 2011). Statistics anxiety is evident in students' attitudes towards the learning of Statistics. It has been found that students' negative attitude towards Statistics is associated with statistical anxiety (e.g., Chiesi & Primi, 2010;Mji & Onwuegbuzie, 2004;Watson et al., 2002).
The psychological processes involved in postgraduate students' development of statistical anxiety are elucidated by the processing efficiency theory, a cognitive-interference approach, and linked to cognitive (worry) and physiological (emotionality) factors (Eysenck, 1979). Concerning the worry component, students entertain fear about statistical tasks they will execute during classroom instructions and assessments. They doubt their capabilities to perform statistical tasks as they engage in self-evaluation. Eysenck explains that this worry makes students to focus on task-irrelevant information rather than task-relevant information, which affects their processing systems. Therefore, highly anxious students would have to deal with many issues, thereby affecting their academic performance. A plethora of empirical evidence (e.g., Davis & Mirick, 2015;Galli et al., 2008;Macher et al., 2012;Chew & Dillon, 2014) have proven that statistical anxiety is associated with poor academic achievement. The anxious moments are displayed through their attitudes-avoidance, nervousness, and tension among others, as explained by the emotionality component.
The increasing high statistical anxiety among postgraduate students raises concerns across all universities in finding reliable ways in addressing the problem at hand. This paper argues that the pedagogical behaviours exhibited by statistics teachers at universities and colleges during instructional periods should be analysed and reported; this is because available evidence points to the fact that classroom factors are significant contributors to postgraduate students' high levels of statistical anxiety, and statistics teachers' poor attitude has been identified as a significant determinant of students' statistical anxiety, among other factors, such as mathematics phobia, disconnection to real life and poor instructional pace (e.g., Pan & Tang, 2005). These factors question the pedagogical behaviours of statistics teachers. Macher et al. (2015) recommended an empirical investigation into the immediate pedagogical behaviours antecedent to students' statistical anxiety.
This study took a broader perspective in addressing students' statistical anxiety from the angle of pedagogy rather than just focusing only on educators' methods of teaching (a component of pedagogy) as recommended by Ghani and Maat (2018). The reason is that teachers are at the centre of classroom interactions and they facilitate the learning process through varied pedagogical prowess. Hence, the approach of profiling statistics teachers' pedagogical behaviours antecedent to students' statistical anxiety might help to comprehensively document appropriate characteristics and practices that statistics teachers must exhibit during Statistics lessons to reduce, if not eliminate, students' increasing statistical anxiety. The current paper, therefore, focused on postgraduate students' level of statistical anxiety and their attitude towards Statistics in light of their teacher's pedagogical behaviours with the ultimate goal of profiling the pedagogical behaviours antecedent to such reported anxiety and attitude.
Following the introduction are the research questions; literature review; research methods and participants; and results, where the paper provides 17 pedagogical behaviours covering teacher characteristics (cognitive and affective factors) as well as pedagogical practices that are needed to reduce postgraduate students' statistical anxiety. After the discussion is presented, conclusions are drawn and recommendations proffered in addressing the problem under study.

Research questions
In order to identify the pedagogical behaviours of statistics teachers that are appropriate for reducing postgraduate students' anxiety, the following research questions were formulated to guide the study.
(1) What is postgraduate students' level of anxiety in studying Statistics courses?
(2) What is postgraduate students' attitude towards Statistics?
(3) Is there a statistically significant influence of postgraduate students' anxiety in Statistics on their attitude towards the study of Statistics?
(4) What teacher pedagogical behaviours are appropriate in reducing postgraduate students' anxiety in Statistics?

Literature review
The increasing statistical anxiety among students, both undergraduate and postgraduate students, seems to downplay the relevance of Statistics courses. For the past two decades, research efforts have been directed towards the development of strategies in addressing the problem. Approaches or strategies developed so far are both cognitive (e.g., Chiou et al., 2014;Miller, 2019) and non-cognitive (Carlson & Winquist, 2011;Dalgleish & Herbert, 2002;Jazayeri et al., 2022;McGrath et al., 2015;Neumann et al., 2009;Pan & Tang, 2004;Segrist & Pawlow, 2007;Williams, 2010) factors that are believed to reduce students' statistical anxiety.
For example, in terms of the cognitive approaches, Chiou et al. (2014) utilised a one-minute paper strategy where students wrote on a paper the important concepts they learnt and indicated unanswered questions at the end of every instructional session. This method was found to be effective in the reduction of undergraduate students' anxiety in Statistics. Also, Miller (2019) indicated that tapping students' cognitive abilities to increase engagement through intelligence-based, creative-based and practical-based instruction is an effective approach to reducing students' statistical anxiety.
Extant literature has documented numerous findings on non-cognitive approaches that helped to reduce students' statistical anxiety. Most of the non-cognitive approaches focused on teaching frameworks and learning approaches. For example, Dalgleish and Herbert (2002) examined the effectiveness of a specific teaching framework on students' anxiety and attitudes towards Statistics in a multivariate Statistics course. The framework included teaching techniques such as the utilisation of real-world examples, enthusiasm, humour and integration of theoretical knowledge and practical skills. Students had the opportunity to use data relevant to their theses. Consequently, a significant reduction was observed in their statistical anxiety. Neumann et al. (2009) confirmed that the integration of humour into instructional techniques enhances students' engagement and learning to reduce students' negative attitudes towards Statistics. Similarly, McGrath et al. (2015) found that when humorous cartoons, statistical music videos, teachers' anecdotes concerning difficulties with Statistics and research on persistence in mathematics are used in a multifaceted teaching framework, students' statistical anxiety will be reduced. In addition to the use of humour, Chew and Dillon (2014) recommended the use of anonymous questions and reduced use of statistical formulas as well as teachers' behaviours such as exhibition of confidence and self-management of anxiety to reduce students' statistical anxiety.
Also, Pan and Tang (2004) found that the combination of application-oriented teaching methods with statistics teachers' concentration on students' anxiety in Statistics is an effective way of reducing their statistical anxiety. Adopting the cooperative learning strategy (mixer) to teach factor analysis, Segrist and Pawlow (2007) found that students' understanding was enhanced as they enjoyed the procedure. Williams (2010) noted that graduate students' anxiety in Statistics was reduced as their instructors used approachable communicative behaviours to interact with them. These approachable communicative behaviours are referred to as immediacy and it is defined as students' perception of instructors' nonverbal and verbal communication skills (Dixon et al., 2016). Earlier, Ruggeri et al. (2008) found that poor communication between statistics teachers and students was the key factor for students' statistical anxiety. Carlson and Winquist (2011) adopted an active learning strategy, known as the curriculum workbook approach (where students read Statistics content before and after classes and worked in groups as they completed statistical problems and responded to conceptual questions) to help improve students' interest and confidence in studying Statistics. In a more recent study, Jazayeri et al. (2022) adopted the integration of web-based intervention and information embedded within a learning management system to heighten students' understanding of statistical concepts and to reduce their statistical anxiety.
So far, literature provides some good measures in addressing students' high statistical anxiety. The measures suggested are both cognitive-focusing on intellectual classroom activities and noncognitive-basically through the use of various teaching frameworks to boost students' interest and confidence in Statistics. However, fundamental gaps must be filled to provide comprehensive measures to address the problem. A critical analysis of the literature shows that most of the approaches adopted to dealing with students' statistical anxiety are through the use of some specific interventions (see, e.g., Jazayeri et al., 2022;McGrath et al., 2015;Pan & Tang, 2004) rather than focusing on the pedagogical behaviours of statistics teachers that are antecedents to students' statistical anxiety. For example, in the case of Segrist and Pawlow (2007), a mixer was used to enhance students' understanding of only factor analysis; this approach appears to lack potency in addressing students' general anxiety in Statistics. This is because concerns are likely to be raised concerning other statistical topics without specific interventions. Also, the approach by Carlson and Winquist (2011) appears to be effective, as it helped to improve students' interest and confidence but leaves out teacher characteristics which can negatively affect students' learning of Statistics. Already, Pan and Tang (2005) cautioned that the attitude of statistics teachers is a critical determinant of students' statistical anxiety. In all these studies, students appear to have been given limited opportunities to comprehensively describe the behaviours of their teachers that are immediate antecedents to their statistical anxiety. Therefore, Macher et al. (2015) recommended an empirical investigation into the immediate pedagogical behaviours antecedent to students' statistical anxiety from different contexts. In terms of time, literature on the teaching interventions that are needed to reduce students' statistical anxiety seems to lack currency, hence the relevance of this study. As a departure from previous studies, the current study focused on students' experiences and perspectives in the investigation of the pedagogical behaviours of their statistics teacher that are immediate antecedent to their (students) statistical anxiety and attitude towards Statistics.

Research design
The sequential explanatory design (follow-up explanations model) was employed with the adoption of the case study strategy to assist with the identification and classification of the pedagogical behaviours of statistics teachers required to reduce postgraduate students' statistical anxiety. The case study strategy allowed for an in-depth and holistic exploration of the pedagogical behaviours exhibited by a university statistics teacher during statistical methods in educational research lessons using multiple sources of evidence (see, Yin, 2018). The university statistics teacher was studied as a case. To affirm that the pedagogical behaviours were antecedents of postgraduate students' low, moderate or high statistical anxiety, their (postgraduate students) statistical anxiety data (quantitative) were first gathered. After, documentary and interview evidence was obtained to explain the observations made during the quantitative phase (see, Creswell & Clark, 2017).

Population, selection of cases, sources of data and ethics
The population was postgraduate students (M.Ed., M.Phil. and PhD candidates) on the distance (N = 28), sandwich (N = 67) and regular (N = 44) modes of education for the 2021/2022 academic year who were taught statistical methods in educational research by the same university statistics lecturer. This statistics lecturer had obtained over six years of teaching experience in handling the course and had helped to improve students' academic performance in Statistics; this prompted the examination of the pedagogical behaviours exhibited by the teacher. Both primary (through a questionnaire and phone interview) and secondary (quality assessment report) data were gathered on the lecturer through postgraduate students. Permission was obtained from the head of the Department responsible for the programmes and the Directorate of Academic Planning and Quality Assurance (DAPQA), University of Cape Coast for the quality assessment report on the statistics lecturer. Respondents and participants were assured of confidentiality and anonymity. During the quantitative and qualitative phases, 99 and 12 (12 yielded the data saturation point, see, Saunders et al., 2018) postgraduate students respectively provided valid data.

Instrumentation
The Statistics Anxiety Rating Scale (STARS) developed by Cruise et al. (1985) was used to gather data on postgraduate students' statistics anxiety and attitude towards Statistics. The STARS has gone through rigorous validation and revisions. Recent validation by Papousek et al. (2012) and Chew et al. (2018) suggested that the instrument even though was developed to measure statistics anxiety, also measured attitude towards Statistics. Hence, the first three subscales -"interpretation anxiety", text and "class anxiety" and "fear of asking for help" should be used to measure statistics anxiety and the last three subscales-"worth of statistics", computation selfconcept' and 'fear of statistics teachers should be used to measure attitude towards Statistics. This recommendation was adhered to in this paper and further validation was carried out to suit the study's context. Figures 1 and 2 display the results of the confirmatory factor analysis.
Again, an unstructured interview guide was used to gather the qualitative data based on the obtained quantitative findings. The guide had only two items: (1) What did you like about your statistics lecturer that made you enjoy Statistics?
(2) What will you consider as good attributes of a statistics teacher to reduce students' anxiety in Statistics?
Both Figures 1 and 2 provide the measurement model information for postgraduate students' statistical anxiety and attitude towards Statistics. The three-model statistical anxiety (Figure 1) and the three-model attitude towards statistics ( Figure 2) examined through Maximum Likelihood with bootstrapping are both approximately fit (see, Hair et al., 2006;Kline, 2016). Table 1 presents the standardised weight, average variance extracted (AVE) and McDonald's omega.  The factor loadings for both constructs generally loaded above the .50 cut-off (see, Hair et al., 2009). Only one item (TCA3) under statistics anxiety and two items (WS3 and FST2) under attitude towards Statistics are below the threshold. However, the item loading above .3 is acceptable. All the loadings are statistically significant. The omega estimates also indicate that all the models' constructs are reliable since they are above .6 (see, Huck, 2004).

Data analysis
The mean and standard deviation were used to describe postgraduate students' statistics anxiety (exogenous variable) and attitude towards Statistics (endogenous variable). Structural equation modelling (SEM) through the analysis of moment structures (AMOS) was used to establish the relationship between postgraduate students' Statistics anxiety (exogenous variable) and their attitude towards Statistics. The re-examination of the intrinsic relationship between the aforementioned variables was to assist in the identification of the pedagogical behaviours (during the qualitative phase of the study) influencing the direction (either low, moderate or high) of students' statistical anxiety. Finally, the qualitative data were inductively analysed into themes to identify the specific pedagogical behaviours of the Statistics teacher.

Results
The quantitative results are first presented after which the qualitative results are presented to provide possible explanations for the findings obtained during the quantitative phase of the study. The statistical anxiety of the postgraduate students was first analysed and the obtained results are presented in Table 2.
Generally, the postgraduate students had a low level of statistical anxiety (M = 2.08, SD = 1.04). It appears that interpretation anxiety and test and class anxiety have the highest tendency to invoke anxious moments in postgraduate students during the study of Statistics. Hence, any practical ways of handling these two factors will help in drastically reducing postgraduate students' statistical anxiety to the barest level. Since data were gathered from students in three modes of study, there might be variations in terms of how they were handled and possibly affect their statistical anxiety. Hence, the influence of their mode of study on their statistical anxiety was examined and Table 3 presents the results. The univariate ANOVA model did not identify postgraduate students' mode of study as a significant factor to create any differences in their statistical anxiety. An examination of the R squared shows that modes of study accounted for a very small variation (.017) in postgraduate students' statistical anxiety (see, Cohen, 1988). The results appear to suggest that the observed low statistical anxiety depended on their teacher's pedagogical behaviours and not the different modes in which they were taught Statistics. A seeming reflection of the low statistical anxiety of the postgraduate students is presented in Table 4, which provides evidence of their attitudes towards the study of Statistics. Table 4 indicates that the postgraduate students who exhibited a low level of statistical anxiety also demonstrated a positive perception to calculate statistics (M = 2.40, SD = 1.11). They valued the worth of Statistics in postgraduate education (M = 2.21, SD = .96), hence, their positive attitude towards the study of Statistics. Therefore, an ostensible positive relationship is created between postgraduate students' statistical anxiety and attitude towards Statistics.  A test of this observation was carried out through SEM using AMOS. Figure 3 presents the obtained structural model and Table 5 presents the detailed results.

Evidence in
The path coefficient and the confidence interval for the exogenous and endogenous variables, thus postgraduate students' interpretation anxiety and attitude (B = .248, 95% CI [.151, .499]), test and class anxiety and attitude (B = .246, 95% CI [.125, .519]), fear of asking for help anxiety and attitude (B = .193,95% CI [.084,.415) show that independently postgraduate students' statistical anxiety subscales have a significant effect on their attitude towards Statistics. By inference, there is a positive relationship between postgraduate students' statistical anxiety and their attitude towards the study of Statistics. Thus, as their statistical anxiety reduces, a corresponding increasing positive attitude will be exhibited towards the study of Statistics. Consequently, a 51% change in postgraduate students' attitudes towards Statistics can be explained by their statistical anxiety; this effect is moderate (Hair et al., 2019).
The low statistical anxiety exhibited by the postgraduate students was further analysed from two data sources: evidence gathered from the DAPQA of the University of Cape Coast and interview data from the students. This was to identify the associated pedagogical behaviours exhibited during Statistics lessons. Table 6 presents the documentary evidence.
The results covered quite a broader area of teacher pedagogical behaviours: right from the design of curriculum plans as reported in the area of statistical course outline to the assessment of students learning in the course. In all aspects, a display of very good performance was reported by the postgraduate students (regular students). As seen, assessment behaviours were significant in the list with the highest mean score (4.00). Assessments were graded, returned and discussed with students in time to support their learning. The interview results (also summarised in Figure 4) give credence to the gathered documentary evidence presented next under identified pedagogical behaviours. This was based on two key questions students answered during the interview:  (1) What did you like about your statistics lecturer that made you enjoy Statistics?
(2) What will you consider as good attributes of a statistics teacher to reduce students' anxiety in Statistics?

Content knowledge in statistics
The prima facie for teaching any subject is the ability to display and command knowledge. The interview participants regarded content knowledge in Statistics as a unique attribute that statistics teachers should have to teach the subject. They (participants) reckoned that their low statistical anxiety was linked to the satisfaction that they had in learning Statistics because of their teacher's content knowledge. As one participant modestly puts it,

Application of theoretical statistical knowledge
Reported statistical lessons that sustained students' interest were not just based on theory as contained in statistical books and literature, but rather an application of the theory to solving problems. In addition, experience knowledge (practical knowledge) was deployed to teach Statistics. As part of the enumeration of the statistics teacher attributes, one of the participants indicated that he also apply the theoretical and practical knowledge of the course to the understanding of the students. [MPhil, Male 2] The students, as reported, appreciated the practical nature in which the Statistics course was taught.

Organised and systematic delivery
The teaching of the course followed an organised and systematic way which elicited students' joy and passion for reading the course. His Statistics in its way is quite complicated and students try to avoid it. So for a teacher to reduce that anxiety, the teacher has to make the students relaxed by presenting the lesson in a simplest manner for students to understand the concepts. [PhD, Female 1]

Teaching passion
The lectures were not just interactive and lively but appeared to be supported by the teaching passion of the statistics teacher. In that, the difficult nature of the subject could not prevent students' development of confidence that they could learn. As honestly narrated, he said

Teaching confidence
The display of teaching confidence during Statistics lessons also assisted to strengthen students' understanding of the course as their interest was boosted. The following are the words of some student participants:

Student engagement
Learning is an active process, which requires students' active participation. Therefore, a teacher's ability to actively engage learners in the teaching and learning process is a hallmark that cannot be disregarded. This student engagement attribute of the teacher would certainly invoke students' preference for learning Statistics. Captured evidence is provided: What I also liked was that he engaged all students in the lesson when he taught.

Effective communication
Refreshing and resounding remarks about the communication abilities of the statistics teacher were equally reported to depict the prominence of effective communication during statistical instructional sessions. Evidence gathered suggests that effective communication creates an interesting classroom environment for students learning of Statistics. This is the undiluted testimony: His ability of command over the English language in his lectures also made me enjoy Statistics class. His body posture and language also keep me enjoying Statistics class.

Student encouragement
In the display of the aforementioned pedagogical attributes by the statistics teacher, which spontaneously reduced their fear of Statistics, the statistics teacher went on to encourage them to appreciate the course. The significance of the course was highlighted to the students for them to appreciate its functional nature and by extension, functional Statistics education. These are the authentic experiences of two student participants: He motivates each student to practice what they have been taught. He encouraged students to accept the course because Statistics can be applied in any discipline. [MPhil, Male 2] He empathizes with learners on topics learners find challenging to comprehend, and encourages learners to study well. [S. M.Ed., Female 2]

Friendliness and patience
A careful analysis of the students' reports highlighted an atmosphere of friendliness and patience in the teaching of Statistics. Yet, the student participants had to categorically emphasize this attribute during the interview:

Acceptance of views
The complexity of knowledge and how one gets to know call for acceptance of views in the teaching and learning process. This attribute was simply displayed by the statistics teacher. The following evidence is provided:

Punctuality and regularity
In all, the statistics teacher exhibited a professional attitude of punctuality and regularity. As

Discussion
The study identified 17 essential pedagogical behaviours, thus teacher characteristics and pedagogical practices that statistics teachers must demonstrate to reduce postgraduate students' statistical anxiety and to nurture in them a positive attitude toward the study of Statistics. The teacher characteristics covered cognitive factors (5 factors) and affective factors (4 factors). The pedagogical practices (8 factors) covered specific classroom teaching behaviours that facilitated postgraduate students' learning of statistics. In ensuring that the pedagogical behaviours of their teacher were immediate antecedents to their statistical anxiety, their statistical anxiety was first examined and the study found that the postgraduate students exhibited a low level of statistical anxiety. These students were drawn from three study modes (regular, sandwich and distance education). However, their study modes did not influence their statistical anxiety. An obvious implication is that the teacher factor (pedagogical behaviours) played a significant role in reducing students' statistical anxiety; this factor is noted as a key determinant of students' statistical anxiety (Pan & Tang, 2005) and a key obstacle for curriculum implementation (Klibthong & Agbenyega, 2018). In this study, the exhibited pedagogical behaviours of the Statistics teacher rather promoted students' satisfaction with learning the course. Consequently, the expected outcome of positive students' attitudes towards Statistics was realised. These findings support the processing efficiency theory (Eysenck, 1979). Students' low level of statistical anxiety reflected in positive emotional tendencies (e.g., satisfaction and passion for studying Statistics), which resulted in a positive attitude towards the study of Statistics. The results from the SEM affirmed and concluded that there exists a positive relationship between students' statistical anxiety and attitude towards the study of Statistics. This means that students' low statistical anxiety resulted in a positive attitude towards the study of Statistics. It is theorised that students' low statistical anxiety will result in a highly positive attitude towards the study of Statistics. A heuristic contribution is made to the application of the processing efficiency theory in addressing students' statistical anxiety in the sense that cognitive factors, affective factors and pedagogical practices of statistics teachers are immediate strategies for reducing students' statistical anxiety.
The qualitative phase of the study attributed the reported outcome to 17 general pedagogical behaviours (immediate antecedents) of their statistics teacher. Five teacher attributes, thus content knowledge in Statistics, practical statistical lessons, application of theoretical statistical knowledge, solving statistical problems and critical explanation of technical statistical terminologies were found and categorised under cognitive factors. The current study further argues that in addition to using cognitive approaches in engaging students to understand statistical concepts (see, for example, Chiou et al., 2014;Dalgleish & Herbert, 2002;Miller, 2019), statistics teachers' content knowledge is critical in preventing likely confusions among students in the course of learning. Postgraduate students need to acquire deep knowledge of statistical concepts and principles in order to exhibit deep understanding when addressing research and statistical problems. More so, the Statistics course is noted for many technical terminologies that create mindwavering problems for students. Hence, students will appreciate statistics teachers who critically explain technical terminologies in Statistics to prevent statistical anxiety.
The affective factors identified four relevant teacher attributes-interactive, humorous and lively lectures, teaching confidence, friendliness and teaching passion to reduce students' statistical anxiety. Confirmation of teacher humour is provided to strengthen existing literature (e.g., Dalgleish & Herbert, 2002;McGrath et al., 2015;Neumann et al., 2009). Teacher confidence is also supported, as found in the literature (e.g., Chew & Dillon, 2014); and friendliness, which communicates teacher approachability (an issue of immediacy) (e.g., Dixon et al., 2016;Williams, 2010). The factor that seems nebulous in the literature is Statistics teachers' teaching passion. The current study highlights teaching passion and this quote is simply remarkable: He is so passionate about his lecture, hence, I also develop passion for Statistics. [D. M.Ed., Male 3]. According to the students, their teacher's teaching passion invoked in them the confidence to learn Statistics. This discovery is in line with theory that teachers' passion has a direct influence on students' passion, which then influences their (students') motivation and achievement (Gilal et al., 2019). Even though the current study did not assess students' achievement in Statistics, the postgraduate students provided oral evidence of their understanding of the course. The argument is that teachers that are passionate about their teaching do express enthusiasm and offer a special type of energy that students pick, it is an infectious type of positivity. Anders (2020) noted that teaching passion is part of the important characteristic of being personable in addition to trying the characteristic of being motivational; this affective teacher characteristic cannot be disregarded in a Statistics classroom.
The last category is teachers' pedagogical practices, comprising eight teacher attributes: organised and systematic delivery; student engagement; effective communication; student encouragement, acceptance of view; punctuality and regularity; promotion of independent study; and prompt assessment feedback and discussion. Even though extant literature (e.g., Dalgleish & Herbert, 2002;McGrath et al., 2015;Miller, 2019;Segrist & Pawlow, 2007) categorically identifies student engagement (through the use of various active learning strategies) and communication attributes (e.g., Ruggeri et al., 2008), the rest are not conspicuously captured. The results on student engagement emphasise that the use of the discovery learning method by way of active learning strategies will be extremely helpful in improving students' understanding of Statistics. In such a pedagogical practice of Statistics teachers, students obtain the opportunity to discover knowledge or facts in Statistics. Postgraduate students' continuous exploration of Statistical knowledge might certainly make them confident and dispel their worry about studying Statistics. This approach to teaching cannot be marginalized since classical literature has already asserted that the books and the teacher were no more the only educators but the hands, eyes and ears (Dewey & Dewey, 1915). By implication, the focus of contemporary teaching should be placed on active learning strategies. Therefore, rethinking how students are engaged during Statistical lessons is a good step in helping them to control their statistical anxiety.
In addition to literature, the current study projects that organised and systematic delivery of Statistics lessons are relevant to reducing students' statistical anxiety. Current evidence indicated that a detailed course outline and simplified statistical notes were used to deliver lessons. This helped to calm the nerves of the students. The following supporting quotes are quite refreshing: His mode of delivery and the fun with which he taught made me to enjoy and love his class. He taught with simplified notes that were explanatory. [D. M.Ed., Male 3]. Statistics in it way is quite complicated and students try to avoid it. So, for a teacher to reduce that anxiety, the teacher has to make the students relaxed, by presenting lessons in a simplest manner for students to understand the concepts. [PhD, Female 1]. The postgraduate students' choice of words (simplified notes) implies that they have remarked on Statistics books and materials as complex, creating learning difficulties. Complex statistical books and materials can easily demotivate students to learn Statistics. Therefore, simplified Statistical notes promote smooth and systematic teaching and learning of Statistics.
In addition, the students appreciated their statistics teacher's effective communication attribute. Communication is the only way a teacher can present understanding to students. Therefore, if poor communication between statistics teachers and students raised students' statistical anxiety (Ruggeri et al., 2008), then an improvement in the communication skills of Statistics teachers can reduce students' increasing statistical anxiety. Finally, the study highlights that assessment strategies can help reduce students' statistical anxiety. Current evidence shows that prompt feedback and discussion of assessment tasks were valued by the students. Immediate constructive feedback helps students to recall materials learnt and improves enrollment and the completion of a degree course among students (LeFebvre & Allen, 2014). Prompt feedback is a critical attribute for assessment for learning Statistics as students get the opportunity to rectify their statistical misconceptions, poor understanding and errors in good time and learn from such mistakes.
In summary, the pedagogical behaviours of statistics teachers are critical antecedents to students' statistical anxiety and attitude towards the study of Statistics. Consequently, students are likely to appreciate the study of Statistics and show low anxiety (regarded as functional anxiety) when 17 pedagogical behaviours are exhibited during the teaching of Statistics. Ostensibly, the affective factors and pedagogical practices augmented the cognitive factors in reducing postgraduate students' level of anxiety in Statistics.

Conclusions
The current study outlined the teaching behaviours Statistics teachers are expected to exhibit during the teaching of Statistics to reduce postgraduate students' anxiety in Statistics. It was noted that postgraduate students' statistical anxiety seems complex, which requires a multifaceted approach to deal with the problem. Therefore, this research is relevant in providing professional support about the pedagogical behaviours Statistics teachers must demonstrate for effective Statistical lessons. The research was grounded on the knowledge that Statistics teachers' pedagogical behaviours are crucial antecedents to students' statistical anxiety. Therefore, it strongly advocates that, in addressing postgraduate students' statistical anxiety, a focus should be placed on Statistics teachers' cognitive factors (content knowledge in Statistics, practical Statistical lessons, application of theoretical Statistical knowledge, solving Statistical problems and critical explanation of technical Statistical terminologies), affective factors (interactive, humorous and lively lectures, teaching passion, teaching confidence, and friendliness and patience) and pedagogical practices (organised and systematic delivery, student engagement, effective communication, student encouragement, acceptance of views, punctuality and regularity, promotion of independent study, prompt assessment feedback and discussion), as shown in the study. If postgraduate students' statistical anxiety is developed cognitively and manifested through their emotions as posited by the processing efficiency theory, then the aforementioned pedagogical behaviours (cognitive factors, affective factors and pedagogical practices) gleaned from postgraduate students' experiences of their Statistics teacher appear highly credible and handy in reducing their (postgraduate students) statistical anxiety, which will help boost their interest and confidence in studying Statistics. This is the heuristic contribution the study offers to the application of the processing efficiency theory. It is believed that this would partly help to sustain the quality of postgraduate students churned out of tertiary institutions for quality scientific data analysis in order to appropriately address societal, business and educational problems.
The study did not consider student-specific factors (entering behaviours) and other environmental factors outside the classroom. Teaching is an interplay between a teacher and students within a context to yield the required results. Hence, focusing only on the pedagogical behaviours of a Statistics teacher might not be enough in addressing the problem of students' statistical anxiety. Hence, this current paper in a way provides leadership for further research in bringing sanity into postgraduate students' statistical anxiety.

Recommendations
The teaching of Statistics courses must be given adequate attention to sustain the credibility of universities and institutions of higher learning as members of the global intellectual community in developing postgraduate students' research and statistical skills. This will help in the development of societies through the advancement of systems, structures and cultures. Hence, statistics teachers should adopt a pluralistic teaching approach that manifests required characteristics (cognitive and affective factors) and effective pedagogical practices to support students' learning of Statistics in a nonthreatening environment. Also, the search for holistic antecedents of postgraduate students' statistical anxiety can take into account other underpinning variables that are not immediate classroom factors of students' statistical anxiety. Most importantly, student-specific factors should be explored.